Problem: Express this product in scientific notation: $(6.10\times 10^{2})\times (3.00\times 10^{-3})$
Answer: Start by collecting like terms together. $= (6.10\times 3.00) \times (10^{2}\times 10^{-3})$ When multiplying exponents with the same base, add the powers together. $= 18.3 \times 10^{2\,+\,-3}$ $= 18.3 \times 10^{-1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $18.3$ is the same as $1.830 \times 10$ $ = {1.830 \times 10} \times 10^{-1} $ $= 1.830\times 10^{0}$